Question

find remainder when x^3+3x^2+3x+1 is divided by 5+2x

Answer 1

by remainder theorem , let f(x) = x^3 +3x^2 + 3x +1 and if (2x + 5) i s divided by f(x) then f(-5/2) = remainder
f(x) = x^3 +3x^2+3x +1
f(-5/2) = (-5/2)^3 +3(-5/2)^2 +3(-5/2) + 1
= (-125/8) + 3(25/4) + 3(-5/2) +1
= (-125 + 150 - 60 +8)/8
= -27/8
or we could also do though long division and answer would be -27/8 or 7/4x +1